Hi: in my younger days, I went to P.P. and it was nice. you had to pay according to your income level. The doc's were great the staff was very friendly and it was very private!!
Good luck!
Either is fine but if you are merely looking for birth control why not see your regular doc. They can handle all your medical needs including your GYN needs.
A good idea would be to go wherever they know you the best. This means that your prescribing dr would have your family history and medical history on hand, so he would be able to look up potential risk factors in a heartbeat.
I would recommend planned parenthood or your doctor as he or she will know you and your history best. He or she can decide on the most suitable pill for you. But ultimately it's your choice, if you wish to see a gyno-go for it!